Name: NOR Gate
Uploaded: 2019-07-19
Duration: 3 min 31 s
Description: sIn this video, let us explore why a NOR gate is considered a universal gate and how we can realise other basic gates through this. Get in to know more.

Question

In a p-n junction diode, the current $I$ can be expressed as
$I = I_{0} \exp (\frac{e V}{k_{B} T} - 1)$

Where, $I_{0}$ is called the reverse saturation current, $V$ is the voltage across the diode and is positive for forward bias and negative for reverse bias, and $I$ is the current through the diode, $k_{B}$ is the Boltzmann constant $(8.6 \times 10^{- 5} e V / K)$ and $T$ is the absolute temperature. If for a given diode, $I_{0} = 5 \times 10^{- 12} A$ and $T = 300 K$ , then

What will be the forward current at a forward voltage of $0.6 V$ ?
What will be the increase in the current if the voltage across the diode is increased to $0.7 V$ ?
What is the dynamic resistance?
What will be the current if reverse bias voltage changes from $1 V$ to $2 V$ ?

Accepted Answer

Given,
The current $I$ in a p-n junction diode, $I = I_{0} \exp (\frac{e V}{k_{B} T} - 1)$
$I_{0} = 5 \times 10^{- 12} A$
$T = 300 K$
$k_{B} = 8.6 \times 10^{- 5} e V / K$
Forward voltage $V = 0.6 V$
The forward current becomes, $I = 5 \times 10^{- 12} \exp (\frac{0.6}{8.6 \times 10^{- 5} \times 300} - 1)$
$\Rightarrow I = 5 \times 10^{- 12} \exp (22.25) = 0.0231 A$
The forward current in the diode is $0.0231 A$ .

For forward voltage $0.7 V$ , current becomes,
$I' = 5 \times 10^{- 12} \exp (\frac{0.7 \times 1.6 \times 10^{- 19}}{1.376 \times 10^{- 23} \times 300} - 1)$
$\Rightarrow I' = 5 \times 10^{- 12} \exp (26.13) = 1. 257 A$

Now the increase in current $= I' - I = 1.257 - 0.0256 = 1.23 A$
The forward current in the diode is $1. 23 A$ .

Dynamic Resistance is given as the ratio of change in voltage and change in current.

$D y n a m i c R e s i s t a n c e = \frac{c h a n g e i n v o l t a g e}{c h a n g e i n c u r r e n t} = \frac{0.7 - 0.6}{1.23} = \frac{0.1}{1. 23} = 0.081 Ω$
If we change the reverse bias voltage from $1 V$ to $2 V$ , then the current will remain the same as $I_{0}$ in both cases. Hence, the dynamic resistance in reverse bias will be infinite

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